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Math 481a Midterm #1. March 16, 2005
Attention! Please, note that this is the closed book test. You are allowed to use a graphing calculator.
In multiple choice, guessing is not penalized. In other problems, please, show all important steps in you
solution.
1a. (5pt) If one is solving the root problem f(x) = 0 by the bisection method, and the initial
interval [a, b] contains two roots, then
the bisection method does not apply;
the bisection section will find only one root;
the bisection method will find the root which is closer to the middle of [a, b];
the bisection method will find the root that is farther from the middle of [a, b];
the bisection method will find both roots.
1b. (5pt) Which from the following is the MINIMUM requirements to guarantee that the fixed
point equation g(x) = x has a solution on [a, b]
g(x) is continuous on [a, b];
g(x) is continuous on [a, b], and the values of g(x) belong to [a, b] (g(x) maps [a, b] into itself);
g(x) is continuous on [a, b], and the values of g(x) belong to [a, b] (g(x) maps [a, b] into itself),
